Concave and Convex Polygons

Date: 08/13/2001 at 23:51:01
From: Jack
Subject: Convex and Concave
What's the difference between convex and concave polygons (or shapes
in general)?
Thank you very much.

Date: 08/14/2001 at 12:01:10
From: Doctor Peterson
Subject: Re: Convex and Concave
Hi, Jack.
A concave figure is one that has an indentation.
This can be stated precisely by considering all line segments joining
any two points in the interior of the figure. If the entire segment
always lies within the figure, then the figure is convex; but if you
can go on a straight line from one point in the interior to another
and pass outside of the boundary, then the figure is concave:
+---------------------+
/ \
/ \
/ \
/ \
/ + \
/ / \
+ / \
\ +----------------+
\ \ /
\ \
\ / \
\ / \
\ + \
\ \
+------------------+
- Doctor Peterson, The Math Forum
http://mathforum.org/dr.math/